I have an RX100. What is the difference between recording video using AVCHD versus MPEG4? Is it a case that one format is better than the other? In which case, which format is superior? Or does each format have its own pros and cons???

AVCHD has 1920 horizontal resolution vs 1440 for MP4.

That's because MP4 uses non-square pixels so that there will be less compression artifacts at the lower data-rate. This was the standard for HDV. It lets you have a lower data rate without having to do as much compression.